Resource Blocks Sharing Model

RBs are assumed to be shared between MNOs based on a contract signed between them. RBs either shared statically, where each MNO accesses only its share of the resources, or dynamically, where MNOs can access the entire set of RBs. As wireless resource virtual- ization is still in its infancy stage, no well-defined sharing models exist yet [80]. Therefore, a general sharing model is assumed based on the following three conditions:

1. In the case of static sharing of RBs, MNOs are assumed to distribute their resources among cells such that the frequency reuse factor is maximized while maintaining a proportional fairness criterion such that

maxX n Λm,n (5.3a) subject to Λm,n+ X c∈Cn Λm,c ≤Ψm,∀n (5.3b) Λm,1 :· · ·: Λm,Nm = (1±α)(Lm,1 :· · ·:Lm,Nm) (5.3c)

where Λm,n is number of RBs allocated to MNO m at RRH n, Lm,n is the load

of MNOm at RRH n, andNm is the set of RRHs that serves the UEs subscribed

to MNO m. The load can be considered as the number of users or a number of packets queued in buffers for the users. As the fluctuation rate of the load in RRHs is slow compared with the transmission time interval (TTI), which is 1 ms in LTE systems for the finest scheduling granularity, the optimization problem in (5.3) can be solved at a coarser granularity than TTI. Other sharing models can be applied here, however, maximizing the frequency reuse factor while considering a fairness criterion is an intuitive target that MNOs are looking to achieve.

2. In case of dynamic sharing of the RBs, the service status of MNO m at RRH n

should be higher than a certain threshold or, if it is not the case, MNO m should access at least Λm,n RBs. This condition ensures isolation between MNOs such

that all MNOs are either satisfied, or can access at least the same number of RBs that they would access in case of static sharing. The service status of an MNO can be related to aspects such as queue length of users’ buffers, spectral efficiency, or energy efficiency.

5.4

Problem Formulation

It is assumed that each MNO aims at maximizing its sum weighted data rates, which is a very common optimization problem in wireless systems [11, 26, 71, 97]. The weights are

selected by MNOs according to their scheduling policies. Assume that userkis connected to RRHn, the scheduling problem can be formulated as

max M X m=1 X n   X k∈Km,n R X r=1 ˆ w_ku_r,kβ_r,k   (5.4a) subject to X c∈Cn X k∈Kc β_r,k + X k∈Kn β_r,k ≤1,∀n, r (5.4b) X r∈R_k T_r,k ≤q_k,∀k (5.4c) (Φm,n >Φthm)or(Ψm,n ≥Λm,n)must hold, ∀(m, n) (5.4d)

whereu_r,k is the data rate achieved by assigning RBrto UEk,wˆ_kis the normalized weight for UEk, Kn = S

m

Km,n is the set of UEs connected to RRH n, Km,n is the set of UEs

subscribed to MNO m and connect to RRH n, Ψm,n is the number of RBs accessed by

MNOmat RRHn, R_k is the set of RBs assigned to UEk, Φm,n andΦthm are the service

status and service status threshold of MNO m at RRH n, and β_r,k is a binary number indicator defined as

β_r,k =

(

1, if RBris assigned to UEk 0, otherwise.

Constraint (5.4b) represents the exclusive constraint which ensures that (i) each RB is assigned to one UE (at most) at each RRH, and (ii) orthogonal sets of RBs are allocated to RRHs that may interfere with each other. It is assumed that the interference is avoided if interfering RRHs are granted orthogonal sets of RBs. Constraint (5.4c) ensures that the transport block size for every UE is less than its unserved data size, whereR_kis the RB set that is assigned to userk. Constraint (5.4d) specifies whether the service status of MNOm

at RRHnis higher than a certain threshold or, if that is not the case, MNOmshould access at leastΛm,n RBs. This constraint ensures isolation between MNOs such that MNOs are

either satisfied, or can access at least the same number of RBs in case of static sharing. It is noteworthy that constraint (5.4d) can be split into two constraints by introducing a binary

variableym,n and a sufficiently large upper boundBm so that

Φm,n >Φthm −Bmym,n (5.5a) Ψm,n ≥Λm,n−Bm(1−ym,n). (5.5b)

Whenym,n = 0, constraint (5.5a) holds, whereas constraint (5.5b) becomesΨm,n ≥ Λm,n −Bm, which is always satisfied if Bm is large enough. Note that the constraint Ψm,n ≥Λm,nmay still be satisfied. Whenym,n = 1, only constraint (5.5b) holds. Conse-

quently, one constraint holds, and the other one may be satisfied.

The formulation in (5.4) allows MNOs to apply different scheduling policies by weighting their UEs differently. In addition, it guarantees that MNOs use their share of RBs at the overloaded RRH. However, if an MNO is underloaded at a specific RRH, its share of RBs can be granted to other MNOs that are overloaded.